Numerical homogenization of monotone elliptic operators

Yalchin Efendiev, Alexander Pankov

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

In this paper we construct a numerical homogenization technique for nonlinear elliptic equations. In particular, we are interested in when the elliptic flux depends on the gradient of the solution in a nonlinear fashion which makes the numerical homogenization procedure nontrivial. The convergence of the numerical procedure is presented for the general case using G-convergence theory. To calculate the fine scale oscillations of the solutions we propose a stochastic two-scale corrector where one of the scales is a numerical scale and the other is a physical scale. The analysis of the convergence of two-scale correctors is performed under the assumption that the elliptic flux is strictly stationary with respect to spatial variables. The nonlinear multiscale finite element method has been proposed and analyzed.

Original languageEnglish (US)
Pages (from-to)62-79
Number of pages18
JournalMultiscale Modeling and Simulation
Volume2
Issue number1
DOIs
StatePublished - Jan 1 2004

Keywords

  • Finite element
  • Homogenization
  • Monotone
  • Multiscale
  • Random

ASJC Scopus subject areas

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications

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